ISRO Scientist Electrical flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Thevenin equivalent resistance

Resistance seen looking into the terminals after deactivating all independent sources; voltage sources become short circuits and current sources become open circuits, while dependent sources stay active.

Maximum power transfer theorem

A load receives maximum power when its resistance equals the Thevenin resistance of the network; at that point the transfer efficiency is 50 percent.

Series resonance condition

At omega = 1/sqrt(LC) the series RLC impedance is purely resistive and minimum, so current is maximum and the quality factor is (1/R)*sqrt(L/C).

Transformer EMF equation

RMS induced EMF equals 4.44 times frequency times peak mutual flux times turns. Volts per turn is fixed by flux and frequency, so core flux depends on applied voltage, not load.

DC machine torque equation

Torque equals P times flux times armature current times conductors divided by 2*pi times parallel paths; for a shunt motor, constant flux makes torque proportional to armature current.

Induction motor slip

Slip equals synchronous speed minus rotor speed, divided by synchronous speed. Rotor frequency equals slip times supply frequency, and rotor copper loss equals slip times air-gap power.

Synchronous machine power angle

For a round-rotor generator, power equals (E_f*V/X_s)*sin(delta). Maximum power transfer occurs at a power angle of 90 electrical degrees.

Per-unit impedance base change

New per-unit impedance equals old per-unit impedance times (S_new/S_old) times (V_old/V_new)^2, where S is base power and V is base voltage.

Ferranti effect

In a long, lightly loaded or open-circuited transmission line, the receiving-end voltage exceeds the sending-end voltage because line charging capacitance causes a voltage rise.

Symmetrical components

Any unbalanced three-phase set decomposes into positive, negative and zero sequence sets. Zero-sequence currents flow only through paths with a neutral return.

Routh-Hurwitz stability criterion

The number of sign changes in the first column of the Routh array equals the number of right-half-plane closed-loop poles, so no sign changes means stability.

Second-order percent overshoot

Percent overshoot equals exp(-pi*zeta/sqrt(1 - zeta^2))*100, where zeta is the damping ratio; peak time is pi divided by damped natural frequency.

Steady-state error type

A type-0 system with a step input has error 1/(1 + K_p); a type-1 system with a ramp has error 1/K_v; a type-2 system with a parabola has error 1/K_a.

Buck converter voltage ratio

In continuous conduction mode, output voltage equals duty cycle times input voltage. The boost converter gives V_in/(1 - D) and the buck-boost gives -V_in*D/(1 - D).

Three-phase controlled rectifier

A fully controlled three-phase bridge in continuous conduction gives average DC voltage of 1.35 times line-to-line RMS voltage times cosine of the firing angle.

V/f induction motor control

Keeping the voltage-to-frequency ratio constant maintains air-gap flux below base speed, giving approximately constant torque; above base speed, field weakening gives constant power.

Op-amp virtual short

With ideal infinite gain and negative feedback, the inverting and non-inverting input voltages become equal, and no current flows into either input terminal.

De Morgan's laws

The complement of a sum equals the product of the complements, and the complement of a product equals the sum of the complements: (A+B)' = A'*B' and (A*B)' = A' + B'.

CMOS dynamic power

Dynamic power equals activity factor times load capacitance times supply voltage squared times switching frequency; static power is negligible because only leakage flows.

Nyquist sampling criterion

A band-limited signal with maximum frequency f_m can be reconstructed exactly only if the sampling rate exceeds twice f_m; otherwise aliasing folds high frequencies into low ones.

Two-wattmeter method

For a balanced three-phase load, total active power is W1 + W2 and reactive power is sqrt(3) times (W1 - W2), where W1 and W2 are the two wattmeter readings.

PMMC meter reading

A permanent-magnet moving-coil instrument responds to the average value of current and is used for DC measurement; a moving-iron meter reads RMS and works on AC.

Paschen's law

Gas breakdown voltage depends on the product of pressure and gap distance; the Paschen curve has a minimum, below which reducing the gap increases breakdown voltage.

Standard lightning impulse

A double-exponential voltage wave with virtual front time 1.2 microseconds and tail time 50 microseconds, used for insulation withstand testing of high-voltage equipment.

Poynting vector

The cross product of electric and magnetic field intensity gives power flow per unit area; the intrinsic impedance of free space is about 377 ohms.

Cayley-Hamilton theorem

Every square matrix satisfies its own characteristic equation, so higher powers of the matrix can be reduced to combinations of lower powers and the identity matrix.

Newton-Raphson convergence

The iteration x_{n+1} = x_n - f(x_n)/f'(x_n) converges quadratically near a simple root; the trapezoidal rule error is order h squared and Simpson's rule order h to the fourth.

Laplace initial value theorem

The initial value x(0+) equals the limit of s times X(s) as s tends to infinity, provided the limit exists; the final value theorem uses s tending to zero.

Successive percentage change

Two successive changes of a percent and b percent give a net change of a + b + a*b/100 percent, where signs indicate increase or decrease.

Syllogism validity

A conclusion is valid only if it follows necessarily from the given premises, regardless of real-world truth; Venn diagrams help test categorical statements.

Binary search complexity

Binary search on a sorted array takes O(log n) comparisons; merge sort and heap sort are O(n log n), while quicksort worst case is O(n squared).

Half adder outputs

A half adder produces sum equal to A XOR B and carry equal to A AND B; a full adder adds a carry-in and can be built from two half adders and an OR gate.